Sharing Hash Codes for Multiple Purposes

Locality sensitive hashing (LSH) is a powerful tool for sublinear-time approximate nearest neighbor search, and a variety of hashing schemes have been proposed for different similarity measures. However, hash codes significantly depend on the similarity, which prohibits users from adjusting the similarity at query time. In this paper, we propose multiple purpose LSH (mp-LSH) which shares the hash codes for different similarities. By using vector/code augmentation and cover tree techniques, our mp-LSH supports L2, cosine, and inner product similarities, and their corresponding weighted sums, where the weights can be adjusted at query time. It also allows us to modify the importance of pre-defined groups of features. Thus, mp-LSH enables us, for example, to retrieve similar items to a query with the user preference taken into account, to find a similar material to a query with some properties (stability, utility, etc.) optimized, and to turn on or off a part of multi-modal information (brightness, color, audio, text, etc.) in image/video retrieval. We theoretically and empirically analyze the performance of three variants of mp-LSH, and demonstrate their usefulness on several real-world data sets.